In mathematics, specifically in category theory, the category of small categories, denoted by Cat, is the category whose objects are all small categories and whose morphisms are functors between categories. Cat may actually be regarded as a 2-category with natural transformations serving as 2-morphisms. The initial object of Cat is the empty category 0, which is the category of no objects and no morphisms. The terminal object is the terminal category or trivial category 1 with a single object and morphism. The category Cat is itself a large category, and therefore not an object of itself. In order to avoid problems analogous to Russell's paradox one cannot form the “category of all categories”. But it is possible to form a quasicategory (meaning objects and morphisms merely form a conglomerate) of all categories. (Wikipedia).
Percentiles, Deciles, Quartiles
Understanding percentiles, quartiles, and deciles through definitions and examples
From playlist Unit 1: Descriptive Statistics
Category Theory: The Beginner’s Introduction (Lesson 1 Video 4)
Lesson 1 is concerned with defining the category of Abstract Sets and Arbitrary Mappings. We also define our first Limit and Co-Limit: The Terminal Object, and the Initial Object. Other topics discussed include Duality and the Opposite (or Mirror) Category. These videos will be discussed
From playlist Category Theory: The Beginner’s Introduction
Categories 6 Monoidal categories
This lecture is part of an online course on categories. We define strict monoidal categories, and then show how to relax the definition by introducing coherence conditions to define (non-strict) monoidal categories. We finish by defining symmetric monoidal categories and showing how super
From playlist Categories for the idle mathematician
Category theory for JavaScript programmers #18: partial orders as categories
http://jscategory.wordpress.com/source-code/
From playlist Category theory for JavaScript programmers
Higher Algebra 7: Non-abelian derived functors
In this video, we discuss the notion of non-abelian derived functors and Animation. Along the way, we discuss the Yoneda lemma. Warning: The Yoneda exercises stated at 35:00 is a bit hard given the technology we have, so I recommend simply proving the analogous statement for ordinary cat
From playlist Higher Algebra
Category Theory: The Beginner’s Introduction (Lesson 1 Video 1)
Lesson 1 is concerned with defining the category of Abstract Sets and Arbitrary Mappings. We also define our first Limit and Co-Limit: The Terminal Object, and the Initial Object. Other topics discussed include Duality and the Opposite (or Mirror) Category. These videos will be discussed
From playlist Category Theory: The Beginner’s Introduction
Category Theory 1.2 : Examples of Categories and Clarification
In this video, I clarify some terminology, and show some very important examples of categories. This includes the category of groups, sets, topologic spaces, monoids, modules, and rings. I also discuss the relation between categories and individual groups, preorders, matrices, and ordinals
From playlist Category Theory
Emily Riehl: On the ∞-topos semantics of homotopy type theory: The simplicial model of...- Lecture 2
HYBRID EVENT Recorded during the meeting "Logic and Interactions" the February 22, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual M
From playlist Topology
Camell Kachour - Globular perspective for Grothendieck ∞-topos and Grothendieck (∞,n)-topos
In this short talk we first briefly recall [4] how to build, for each integers n0, monads Tn on the category Glob of globular sets which algebras are globular models of (1; n)-categories, which have the virtue to be weak 1-categories of Penon and thus also to be weak 1-categories of Batani
From playlist Topos à l'IHES
Julia Plavnik: "Classifying small fusion categories"
Actions of Tensor Categories on C*-algebras 2021 "Classifying small fusion categories" Julia Plavnik - Indiana University, Mathematics Abstract: Classifying fusion categories is a problem that at the moment seems out of reach, since it includes the classification of finite groups and sem
From playlist Actions of Tensor Categories on C*-algebras 2021
Higher Algebra 1: ∞-Categories
In this video, we introduce ∞-categories. This is the first of a series of videos towards a reasonably non-technical overview over stable ∞-categories and Higher Algebra, which are intended to be watchable independently from the main lecture. Further resources: M.Boardman and R.Vogt. Homo
From playlist Higher Algebra
Locally Cartesian Closed Infinity Categories - Joachim Kock
Joachim Kock Universitat Autonoma de Barcelona February 21, 2013 For more videos, visit http://video.ias.edu
From playlist Mathematics
Emily Riehl: On the ∞-topos semantics of homotopy type theory: All ∞-toposes have... - Lecture 3
HYBRID EVENT Recorded during the meeting "Logic and Interactions" the February 24, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual M
From playlist Topology